1

Simple Keynesian Model

National Income DeterminationTwo-Sector National Income

Model

2

Outline Macroeconomics [2.1] Exogenous & Endogenous Variables

[2.3] Linear Functions [2.6] Aggregate Demand & Supply [3.2] National Income Determination

Model OR Simple Keynesian Model [3.3]

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Outline National Income Identities [3.4] Equilibrium Income [3.5 & 3.11] Consumption Function [3.6] Investment Function[3.7] Aggregate Demand Function [3.8]

4

Outline Output-Expenditure Approach to

Income Determination[3.9 ] Expenditure Multiplier [3.9] Saving Function [3.10] Injection-Withdrawal Approach to

Income Determination [3.10] Paradox of Thrift [3.13]

5

Macroeconomics National income, general price

level, inflation rate, unemployment rate, interest rate and the exchange rate are the economic measures to be explained in the macroeconomic models / theories

6

Exogenous & Endogenous Variables

Exogenous Variable the value is determined by forces outside

the model any change is regarded as autonomous I, G, X ( Micro: Income/Population)

Endogenous Variable the value is determined inside the model factor to be explained in the model Y, C, M ( Micro: Price/Quantity)

7

Linear Functions A function specifies the

relationship between variables y is the dependent variable x is the independent variable y=f(x)

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Linear Functions y=f(x) y= c y=mx y=c+mx m, c are exogenous variables y, x are endogenous variables

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Linear Functions Consumption Functions C= f(Y) C= C’ C= cY C= C’ + cY

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Linear Functions C’, c are exogenous variables C, Y are endogenous variables Y is independent variables C is dependent variables

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Linear Functions Can you express the 3

consumption functions graphically?

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Linear Functions The parameter C’ is autonomous

consumption It summarizes the effects of all factors

on consumption other than national income.

What is the difference between a change in exogenous variable (autonomous change) and a change in endogenous variable (induced change)?

13

Linear Functions C= f(Y, W) If wealth is deemed as a relevant

factor but is not explicitly included in the consumption function C=C’+ cY

a rise in wealth W will lead to a rise in the exogenous variable C’

graphically, the consumption function C will shift upwards

14

Linear Functions What happens if c ? What happens if Y ?

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Linear Functions Consumption function can also be

a relationship between consumption C and interest rate r.

What do you think of the relationship between the variables, i.e., consumption C and interest rate r?

Are they positively correlated or negatively correlated?

16

Aggregate Demand & Supply Aggregate Demand

the relationship between the total amount of planned expenditure and general price level (v.s. aggregate expenditure E)

Aggregate Supply the relationship between the total

amount of planned output and the general price level

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Aggregate Demand & Supply

Price Level

National Output

Aggregate Supply

Aggregate Demand

Equilibrium: no tendency to change and

the values of the endogenous variables

will remain unchanged in the absence of

external disturbances

18

Aggregate Demand & Supply

P

Y

AS

AD1

AD2

Yf

When AS is vertical

A shift of AD will cause a change

In P only but have no effect on Y

19

Aggregate Demand & Supply

P

Y

AS

AD1 AD2 When AS is horizontal

A shift of AD will cause a change in Y only but have no effect on P

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Aggregate Demand & Supply

AD AS

YfYe

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Aggregate Demand & Supply The Upward Sloping AS

When the economy is close to but below full employment level Y < Yf, the attempt to raise output by increasing aggregate demand will face supply side limitations

both price and output will increase

22

Aggregate Demand & Supply The Vertical AS (slide 18)

When full employment is attained Y = Yf, an increase in aggregate demand can only cause prices to rise

23

Aggregate Demand & Supply The Horizontal AS (slide 19)

When output is far below Yf, the equilibrium output is determined by AD

The supply side has no effect on income level as firms could supply any amount of output at the prevailing price level

The Keynesian Model analyses the situation of an economy with fixed prices and high unemployment Y < Yf

24

National Income Determination Model Assumptions:

National income Y is defined as the total real output Q

A constant level of full national income Yf

Serious unemployment, i.e., there are many idle or unemployed factors of production

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National Income Determination Model (cont’d)

Income / output can be raised by using currently idle factors without biding up prices

Price rigidity or constant price level There are only households and firms

(2-sector). No government and foreign trade

26

National Income Identities An identity is true for all values of the

variables In a 2-sector economy, expenditure

consists of spending either on consumption goods C OR investment goods I.

Aggregate expenditure (AE OR E) is ,by definition, equal to C plus I

E C + I

27

National Income Identities National income Y received by

households, by definition, is either saved S OR consumed C.

Y C + S

28

National Income Identities Aggregate expenditure E is, by

definition, equal to national income Y

Y E C + S C + I S I

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Equilibrium Income Equilibrium is a state in which there is

no internal tendency to change. It happens when

firms and households are just willing to purchase everything produced Y = E (v.s. Micro: Qs = Qd) [slide 30-36]

Income-Expenditure Approach [slide 37-60] planned saving is equal to planned

investment S = I Injection-Withdrawal Approach [slide 61-74]

30

Equilibrium Income What is the definition of GNP (/

GDP) in national income accounting?

The total market value of all final goods and services currently produced by the citizens (/within the domestic boundary) of a country in a specified period

31

Equilibrium Income Ex-ante Y > E Excess supply

planned output > planned expenditure unexpected accumulation of stocks OR unintended inventory investment OR involuntary increase in inventories

In national income accounting, this amount Y-E is treated as (unplanned) investment by firms

32

Equilibrium Income Ex-post Y= E

Actual (Realised)= Planned + UnplannedExpenditure ExpenditureInvestment

Actual (Realised) Output = Actual Expenditure

Firms will reduce output

33

Equilibrium Income Ex-ante Y < E Excess Demand

planned output < planned expenditure

unexpected fall in stocks OR unintended inventory dis-investment OR involuntary decrease in inventories

However, in national income accounting, this amount E - Y consumed is not currently produced

34

Equilibrium Income Ex-post Y= E

Actual (Realised)= Planned - UnplannedExpenditure Expenditure Dis-investment

Actual (Realised) Output = Actual Expenditure

Firms will increase output

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Equilibrium Income Ex-ante Y= E Equilibrium There is no unintended inventory

investment OR dis-investment Ex-post Y=E

36

Equilibrium Income When there is excess supply, i.e., planned

output > planned expenditure, firms will reduce output to restore equilibrium

When there is excess demand, i.e., planned expenditure > planned output, firms will increase output to restore equilibrium

In the Keynesian model, it is aggregate demand that determines equilibrium output. Remember the horizontal AS [slide 19]

37

Consumption Function Now, we will look at the 1st

component of the aggregate expenditure E C + I i.e. C

Empirical evidence shows that consumption C is positively related to disposable income Yd

Yd = Y since it is a 2-sector model Remember the 3 consumption

functions [slide 9 & 11]

38

Consumption Function Autonomous Consumption C’

It exists even if there is no income. This can be done by dis-saving, i.e., using the past saving

Then, saving will be negative when income is zero.

It is totally determined by forces outside the model

What happens to the 3 consumption functions if C’ ? Or C’ ?

39

Consumption FunctionC’ = y-intercept

In C’

C = C’ C = cY C = C’ + cY

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Consumption Function Marginal Propensity to Consume MPC = c

It is defined as the change in consumption per unit change in income

MPC = C / Y It is the slope of the tangent of the consumption

function For a linear function, MPC is a constant What does the consumption function C look like if

MPC is increasing? Decreasing? It is assumed that 0 < MPC < 1 What happens to the 3 consumption functions if

c ? or c ?

41

Consumption FunctionMPC = slope of tangent

in MPC or in c

C = C’ C = cY C = C’ + cY

42

Consumption Function Average Propensity to Consume APC

It is defined as the ratio of total consumption C to total income Y

APC = C / Y It is the slope of ray of the consumption

function When C = C’ OR C = C’ + cY, APC

decreases when Y increases. When C = cY, APC = MPC = c =

constant

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Consumption FunctionAPC = slope of ray

C = C’ C = cY C = C’ + cY

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Consumption Function Relationship between APC and MPC C = C’ Divide by Y C/Y = C’/Y APC = C’/Y APC when Y Slope of ray flatter when Y Slope of tangent = MPC = c = 0

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Consumption Function Relationship between APC and MPC C = cY Divide by Y C/Y = c APC = MPC = c Slope of ray=Slope of

tangent=constant=c

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Consumption Function Relationship between APC and MPC C = C’ + cY Divide by Y C/Y = C’/Y + c APC = C’/Y + MPC C’ +ve APC > MPC Slope of ray steeper than slope of tangent Slope of tangent constant Slope of ray flatter when Y APC when Y

47

Investment Function Let’s look at the 2nd component of

the aggregate expenditure E C + I

An investment function shows the relationship between planned investment I and national income Y

It can be a linear function or a non-linear function

48

Investment Function Again, there can be 3 investment functions I = I’ I = iY I = I’ + iY Economists usually use the first one, i.e.,

I= I’ as investment is thought to be correlated with interest rate r, instead of Y

I’ , i are exogenous variables I , Y are endogenous variables

49

Investment Function Autonomous Investment I’ It is independent of the income

level and is determined by forces outside the model, like interest rate.

I’ is the y-intercept of the investment function

50

Investment Function Marginal Propensity to Invest i It is defined as the change in investment

I per unit change in income Y MPI = I / Y MPI would not correlate with Yd It is the slope of tangent of I It is also determined by forces outside

the model

51

Investment Function

MPI = i =slope of tangent

I’ = y-intercept

I = I’ I = iY I = I’ + iY

API when Y

MPI =0

52

Aggregate Expenditure Function

Given E = C + I C = C’ + cY I = I’ E = I’ + C’ + cY E = E’ + cY

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Aggregate Expenditure Function

I = I’ C = C’+cY E = I’ + C’+ cY

C, I, EI C

Y

Slope of tangent=0

Slope of tangent = c

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Aggregate Expenditure Function Autonomous Change When C’ or I’ E’ shift upward When c slope of E steeper

rotate Induced Change When Y E move along the

curve

55

Output-Expenditure Approach National income is in equilibrium

when planned output = planned expenditure

We have planned expenditure E=C+I Equilibrium income is Ye=planned E A 45°-line is the locus of all possible

points where Y = E When E = planned E, Y = Ye

56

Output-Expenditure Approach

Y = E Planned E=C +I

Y

C, I, E

Y=planned EPlanned E>Y

Unintended inventory dis-investment

Actual E =Y

Ye

Planned E < Y

Unintended inventory investment

Actual E = Y

Y Y

57

Output-Expenditure Approach Y = planned E Y = I’ + C’ + cY Y = E’ + cY (1-c)Y = E’ Equilibrium condition Y = E’

11-c

58

Output-Expenditure Approach If C’ or I’ E’ E Ye If c E steeper Ye If we differentiate the equilibrium

condition, Y/E’ = 1/(1-c) Given 0 < c < 1 1/(1-c) > 1 E’ Ye by a multiple 1/(1-c) of E’

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Expenditure Multiplier 1/(1-c) Assume c=0.8, E’ = 100 The one who receive the $100 as

income will spend 0.8($100) then the one who receives 0.8($100)

as income will spend 0.8*0.8($100) The process continues and the total

increase in income is $100+0.8($100) +0.8*0.8($100) +

…

60

Expenditure Multiplier 1/(1-c) The total increase in income is

actually the sum of an infinite geometric progression which can be calculated by the first term divided by (1- common ratio)

The first term here is E’ = $100 and the common ratio is c =0.8

The sum of GP is E’ * multiplier

61

Saving Function We have Y C + S [slide 27] Saving function can simply be derived

from the consumption function S = Y – C if C = C’ + cY S = Y – C’ – cY S = -C’ + (1-c) Y S = S’ + sY S’= -C’ s = 1 - c S’ < 0 if C’ >0 S’ = 0 if C’ = 0

62

Saving Function

Y*

S’

Y Y

S SS = sY

S = (1-c)Y

S = S’+ sY

S =-C’+(1-c)Y

Slope of tangent = s =1- c

Slope of ray = slope of tangent

Slope of ray < slope of tangent

Y > Y* S+ve

63

Saving Function Autonomous Saving S’ Since S= -C’ + (1-c)Y

If C’= 0 when C= cY S = (1-c)Y S’ = 0

If C’ +ve when C = C’ + cY S = -C’ + (1-c)Y S’ –ve

If Y= 0 S’ = -C’ Dis-saving

64

Saving Function Marginal Propensity to Save MPS = s It is defined as the change in saving per

unit change in disposable income Yd OR income Y (in a 2-sector model)

MPS = S/ Y It is the slope of tangent of the saving

function MPS is a constant if the consumption /

saving function is linear

65

Saving Function Average Propensity to Save APS It is defined as the total saving

divided by total income APS = S/Y It is the slope of ray of the saving

function

66

Saving Function Average Propensity to Save APS (cont’d) When S= sY APS = MPS = s = constant

When S=S’+ sY APS < MPS as S’ –ve APS –ve when Y < Y* [slide 62] APS = 0 when Y = Y* APS +ve when Y > Y* APS when Y

67

Saving Function Y = C + S Differentiate wrt. Y Y/Y=C/Y + S/Y 1= MPC + MPS 1 = c + s [slide 61]

S = S’ + sY Divided by Y S/Y = S’/Y + s APS=S’/Y+MPS [slide 66]

68

C

Y = E

Y*=CY<C Y>C

-ve S

+ve S

How to determine Ye?

Ye

Planned Y = planned E

Planned C

Planned I

Y

C, S, I, E

69

C

Y = E

Ye

Planned C

Planned I

E = C + I

Planned Y < Planned E

Y = C S =0 No Dis-saving Y < E Unintended Inventory Dis-investment Actual I =Planned I – Unintended I

Y < C

Y < E

70

C

Y = E

Ye

Planned C

Planned I

E = C + I

Y > C S +ve Saving Y > E Unintended Inventory Investment Actual I =Planned I + Unintended I

Planned Y > Planned EHow about Y*<Y<Ye?

71

Injection-Withdrawal Approach Remember the national income

identity S I [slide 28] The equilibrium income happens

when planned Y= planned E as well as planned S = planned I [slide 29]

72

Injection-Withdrawal Approach

S’+ sY = I’ sY = I’ – S’ S’=-C’ s=1-c (1-c)Y = I’ + C’ = E’ Equilibrium condition [slide 57] Y = E’ 1

1-c

73

Equilibrium Income No matter which approach you

use, you will get the same equilibrium condition.

Can you derive the equilibrium condition if investment I is an induced function of national income Y, using the 2 approaches?

74

Equilibrium Income Write down the investment function I first.

Then write down the saving function S. Remember planned S = planned I when Y is in equilibrium {Injection-Withdrawal}

Write down the investment function I as well as the consumption function C. Together they are the aggregate expenditure function E. Remember planned Y = planned E when Y is in equilibrium {Output-Expenditure}

75

Injection-Withdrawal Approach

76

Output-Expenditure Approach

77

Y=E

E=C+I

C=C’+cY

I=I’I’C’

E’=C’+I’

Y<C Y>CY=C

S = S’ + sY

S’=- C’

78

E=C+I

I=I’I’

E’=C’+I’

S=S’+sY

Planned Y=Planned E

Planned S=Planned I

Unintended Inventory Investment

Unintended Inventory Investment

Unintended Inventory Disinvestment

Unintended Inventory Disinvestment

79

Paradox of Thrift This is an example of the “fallacy of

composition” “Thriftiness, while a virtue for the

individual, is disastrous for an economy” Given I = I’ Given S = S’ + sY OR S = -C’ + (1-c)Y Now, suppose S’ Will Ye increase as well?

80

I=I’

S= S’+ sY

S=S” +sY

Ye

Excess Supply

A rise in thriftiness causes a decrease in national income but no increase in realised saving.

81

Paradox of Thrift If a rise in saving leads to a reduction in

interest rate and hence an increase in investment (Think of the loanable fund market), national income may not decrease

Ye will increase if I’ increase more than S’ Ye will remain the same if I’ increase as much

as S’ Ye will decrease if I’ increase less than S’

82

I=I’

S= S’+ sY

S=S” +sY

Ye

I=I”

I > S

83

I=I’

S= S’+ sY

S=S” +sY

Ye

I=I”

=Ye

I = S

84

I=I’

S= S’+ sY

S=S” +sY

Ye

I=I”

The reduction in Ye is less than the case when I does not increase

What about the case if I is an induced function of Y?

I < S